Showing papers in "American Journal of Physics in 1972"
1,033 citations
TL;DR: In this article, the authors present a paperback edition of a distinguished book, originally published by Clarendon Press in 1971, which is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another.
Abstract: This is a paperback edition of a distinguished book, originally published by Clarendon Press in 1971. It was then the first text on critical phenomena, a field that has enjoyed great activity for the past twenty years and that still continues to attract much attention. The book is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another. (A simple example is the melting of a solid to become a liquid.) Such a transformation is termed 'critical' when, after a certain amount of the substance changes phase, the entire bulk virtually instantaneously also makes the transition. A second, updated edition is planned for future publication, but in the mean time this paperback reissue will be useful in teaching the fundamental principles of this extremely interesting subject.
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TL;DR: In this paper, the Copenhagen interpretation of quantum theory is discussed and an attempt is made to give a coherent account of the logical essence of this interpretation, which is the case in the case of quantum physics.
Abstract: An attempt is made to give a coherent account of the logical essence of the Copenhagen interpretation of quantum theory. The central point is that quantum theory is fundamentally pragmatic, but nonetheless complete. The principal difficulty in understanding quantum theory lies in the fact that its completeness is incompatible with external existence of the space-time continuum of classical physics.
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TL;DR: In this paper, a numerical solution to the Schrodinger equation can be introduced to undergraduate students at the junior level, and an extension of the method to inhomogeneous equations and self-consistent field calculations is briefly mentioned.
Abstract: Numerical solution to the Schrodinger equation can be introduced to undergraduate students at the junior level. Numerov process is discussed in detail for the homogeneous differential equation and an extension of the method to inhomogeneous equations and self-consistent field calculations is briefly mentioned. An application to the simple harmonic oscillator is given as an example.
TL;DR: In this article, a theory for acoustic radiation pressure exerted by a plane wave on a perfect absorber, using Euler's momentum theorem, was developed for the case of an open vessel, the radiation pressure P equals the mean energy density E even when nonlinearities of the medium and distortion of wave form are taken into account.
Abstract: A theory is developed for acoustic radiation pressure exerted by a plane wave on a perfect absorber, using Euler's momentum theorem. For the case of an open vessel, the radiation pressure P equals the mean energy density E even when nonlinearities of the medium and distortion of wave form are taken into account. For a closed vessel P equals [1 + 12(B/A)]E. The term B/A describes the non-linearity in the pressure-density relation for the medium and equals γ−1 for the case of an ideal gas under adiabatic conditions.
TL;DR: In this article, the authors reviewed the Galilean invariance of nonrelativistic laws with particular attention given to the transformation properties of field-theoretic quantities, and showed that these laws retain their form under coordinate transformations to noninertial frames which move with arbitrary accelerative translational motion (without rotation) with respect to inertial frames.
Abstract: The Galilean invariance of nonrelativistic laws is reviewed with particular attention given to the transformation properties of field-theoretic quantities. It is then shown that Galilean-invariant nonrelativistic laws generally manifest a broader covariance, the laws retaining their form under coordinate transformations to noninertial frames which move with arbitrary accelerative translational motion (without rotation) with respect to inertial frames.
TL;DR: Elements of Neutron Interaction Theory as mentioned in this paper is a first-year textbook for graduate students in nuclear engineering, dealing with the interactions of neutrons, photons, and charged particles with nuclei, atoms, and electrons.
Abstract: "Elements of Neutron Interaction Theory" is a first-year textbook for graduate students in nuclear engineering, dealing with the interactions of neutrons, photons, and charged particles with nuclei, atoms, and electrons. The aim of the book is to present, as simply as possible, those aspects of neutron interaction theory which follow directly from conservation laws and elementary quantum mechanics. It is intended to be understood by anyone who has obtained the equivalent of a bachelor's degree in physics, chemistry, or one of the engineering disciplines. No mathematical background beyond differential equations and elementary vector analysis and no physics background beyond elementary modern physics is assumed.
TL;DR: The role of museums in science education is discussed in this article, with particular reference to the Exploratorium in San Francisco, where art, an atmosphere of playfulness, and exhibits about the mechanisms of human sensory perception have figured in the development of the museum.
Abstract: The role which museums can play in science education is discussed in general and with particular reference to the Exploratorium in San Francisco. We describe how art, an atmosphere of playfulness, and exhibits about the mechanisms of human sensory perception, have figured in the development of our museum. It is suggested that some of the objectives of interdisciplinary survey science courses can best be achieved in museum like settings where students and general public alike can gain firsthand experience with the fabric of natural phenomena.
TL;DR: In this article, a review of different approaches to the problem of an infinitesimally extended accelerating physical object is presented, where the central problem is in taking successive Lorentz transformations between parallel coordinate systems and clearly distinguishing between physical rotations of the object and coordinate rotations.
Abstract: This paper is intended to give a simple physical understanding of the kinematic effect referred to as the Wigner rotation or, when applied to an orbiting object, the Thomas precession. Since this is a kinematic effect it applies not only to particles with spin but to all physical bodies in which a direction can be defined. To aid in avoiding the usual pitfalls in working with these problems, a review is made of several different approaches to the problem of an infinitesimally extended accelerating physical object. The central problem is in taking successive Lorentz transformations between parallel coordinate systems and clearly distinguishing between physical rotations of the object and coordinate rotations. When accounting for the energy associated with the Thomas precession a simple physical explanation is given rather than the misleading description popularly presented.
TL;DR: A simple analysis of the Goos-Hanchen effect involving only elementary concepts of classical mechanics is presented in this paper, where the authors show that it is a very simple process involving only simple concepts of mechanics.
Abstract: A very simple analysis of the Goos-Hanchen effect, involving only elementary concepts of classical mechanics, is presented.
TL;DR: Einstein's arguments concerning the interpretation of quantum mechanics are reviewed and contrasted with certain misconceptions regarding his attitude toward the theory as discussed by the authors, and some definite physical arguments which did not assume determinism.
Abstract: Einstein's arguments concerning the interpretation of quantum mechanics are reviewed and contrasted with certain misconceptions regarding his attitude toward the theory. He considered Born's statistical interpretation to be the only satisfactory one, and he was not a supporter of hidden-variable theories such as that of Bohm. His criticism of the interpretation accepted, at least tacitly, by many physicists was that the quantum state function does not provide a description of an individual system but rather of an ensemble of similar systems. This criticism was not based merely upon his famous remark that God does not play dice, but upon some definite physical arguments which did not assume determinism.
TL;DR: In this article, it is argued that the problem of measurement arises because the precise, mutually exclusive conditions for these two types of transitions to occur are not specified within orthodox quantum mechanics, and that if the measurement is to be resolved, a new, fully objective version of quantum mechanics needs to be developed which does not incorporate the notion of measurement in its basic postulates at all.
Abstract: According to orthodox quantum mechanics, state vectors change in two incompatible ways: “deterministically” in accordance with Schr0dinger's time-dependent equation, and probabilistically if and only if a measurement is made. It is argued here that the problem of measurement arises because the precise, mutually exclusive conditions for these two types of transitions to occur are not specified within orthodox quantum mechanics. Fundamentally, this is due to an inevitable ambiguity in the notion of “measurement” itself. Hence, if the problem of measurement is to be resolved, a new, fully objective version of quantum mechanics needs to be developed which does not incorporate the notion of measurement in its basic postulates at all.
TL;DR: In this article, the Buckingham pi theorem has been applied to the heat equation in spherical coordinates and one dimensional gas motion without boundary conditions, and it has been shown to be useful in physics.
Abstract: Working from a simple example of a dimensional transformation, the essential elements are identified, and an abstract prototype transformation is defined. With the aid of careful definitions and a geometric interpretation of what happens in a dimensional transformation the Buckingham pi theorem is written down but not proved. The application of this theorem to the heat equation in spherical coordinates and one dimensional gas motion without boundary conditions serve to illustrate the usefulness of the theorem in physics.
TL;DR: In this article, a simple and conceptually clear proof of the inverse Noether's theorem is presented, both for classical point mechanics and for classical field theory, starting from an analysis of the time dependence (of the four divergence, respectively), of an arbitrary dynamical quantity, to relate it to the variation of the action integral induced by a suitably defined infinitesimal transformation.
Abstract: A simple and conceptually clear proof of the inverse Noether's theorem is presented, both for classical point mechanics and for classical field theory. We start from an analysis of the time dependence (of the four divergence, respectively), of an arbitrary dynamical quantity, to relate it to the variation of the action integral induced by a suitably defined infinitesimal transformation. When the dynamical quantity is chosen to be a constant of motion (a divergenceless quantity, respectively), this infinitesimal transformation is shown to act as an invariance transformation on the dynamical system.
TL;DR: A continuation of the modernized presentation of Poincare's Rendiconti paper (begun in the November 1971 issue of this Journal) can be found in this paper.
Abstract: This is a continuation of the modernized presentation of Poincare's Rendiconti paper (begun in the November 1971 issue of this Journal). It covers Secs. 5–8 of that paper, dealing with its central theme, as indicated by its title, “On the dynamics of the electron,” the subject being of interest to both the historian of the classical theory of the electron and the historian of relativity.
TL;DR: Newman's best year, 1665, was celebrated at the Conference on Newtonian Studies at the University of Texas as discussed by the authors, where a number of scholars contributed evaluations of Newton's world within the framework of modern science.
Abstract: At the beginning of 1665, when Isaac Newton was twenty-three years old, he returned to his native village for a period of two years to escape the plague that had closed down Cambridge University. He later wrote that these years were his most fruitful and creative, and recalls in particular that in 1666 he developed the integral calculus, experimentally verified the composite nature of light, and refined his gravitational theory to the point that he was able to satisfy himself through calculation that the earth's gravity holds the moon in orbit. Recent Newtonian scholarship has effectively called his memory into question somewhat on these points, but the "marvelous year" of 1666 may surely be taken as symbolic of a decisive turning point in the history of human thought.Three hundred years later, in order to commemorate Newton's best year by considering the whole of his life, work, outlook, and influence, the Conference on Newtonian Studies was held at the University of Texas. The articles in this book, many since expanded or revised, were originally prepared for that event. Their authors include not only Newton specialists but, in order to provide the widest perspective, general historians of ideas, of science, of art, of philosophy and religion, were invited as well. Several philosophers of science and practicing physicists have contributed evaluations of Newton's world within the framework of modern science.Another group of scholars was invited to write brief critical comments on most of the articles, and the dialogue that results, often spirited, will invite the reader to join in.The major articles and their authors are as follows: Introduction, Robert Palter. "I. Newton's Life and Society: " The Lad from Lincolnshire, Frank E. Manuel. Newton and His Society, Christopher Hill. "II. Newton's Scientific Achievements: " Newton and the Theory of Matter, A. Rupert Hall and Marie Boas Hall. Sources and Strengths of Newton's Early Mathematical Thought, D. T. Whiteside. Uneasily Fitful Reflections on Fits of Easy Transmission, Richard S. Westfall. Newton's and Leibniz' Dynamics, Pierre Costabel. Newton's Achievements in Dynamics, John Herivel. Newton's Second Law and the Concept of Force in the "Principia, " I. Bernard Cohen. Reactions of Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's "Principia, " C. Truesdell. Newtonian Cosmology, E. L. Schucking. "III. Philosophical Analysis of Newton's Scientific Achievements: " Newton and the Inductive Method, Robert Palter. Newtonian Space-Time, Howard Stein. The Philosophical Significance of Newton's Science, Dudley Shapere. "IV. Newton's Influence: " The Apotheosis of Newton in Art, Francis Haskell. Mechanical Philosophy and Hypothetical Physiology, William Coleman. The Religious Consequences of Newton's Thought, John Herman Randall, Jr.The critical comments were written by David Hakes, Lawrence Stone, Asger Aaboe, Thomas S. Kuhn, J. M. Briggs, Jr., Gerd Buchdahl, J. E. McGuire, A. E. Woodruff, and Jurgen Ehlers.
TL;DR: In this paper, the authors show that the time recorded by an ideal clock after a circumnavigation of the Earth depends not only on the speed and altitude but also on the direction and ground speed of the clock.
Abstract: Relative to a clock at rest on the Earth's surface, the time recorded by an ideal clock after a circumnavigation of the Earth depends not only on the speed and altitude but also on the direction of the circumnavigation and on the rotational speed of the Earth. Such a clock may run either fast or slow, depending on the direction and ground speed for the circumnavigation. This directional dependence should be perceptible with commercial jet speeds and cesium beam clocks.
TL;DR: In this article, the perturbation of atomic hyperfine levels by a weak uniform static electric field is discussed, and the effects linear in the field are identically zero and the levels suffer small shifts proportional to the square of the field.
Abstract: The perturbation of atomic hyperfine levels by a weak uniform static electric field is discussed. For nearly all atoms, the effects linear in the field are identically zero, and the levels suffer small shifts proportional to the square of the field. The calculation of these shifts using ordinary second-order time-independent perturbation theory is presented. The advantages of separating the interaction into kinematical and dynamical parts and techniques for performing the separation are discussed. The algebra of irreducible spherical tensors is used to separate the interaction into parts having monopolar and quadrupolar symmetry. Some numerical values of the matrix elements of the quadrupole part are given (the monopole elements are trivial), and the shifts of the hyperfine levels due to this interaction are plotted as a function of field for some typical atoms.
TL;DR: In this paper, a theoretical analysis for a chain-collision process occurring in a one-dimensional arrangement of objects having, in general, different masses, when independent collisions are assumed is presented.
Abstract: A theoretical analysis is presented for a chain-collision process occurring in a one-dimensional arrangement of objects having, in general, different masses, when independent collisions are assumed. Expressions for the velocity and momentum gains and the energy transfer are derived and applied to configurations with various mass ratios between neighboring objects. Intriguing transformation properties are displayed by these quantities under the permutation operation. These effects are shown to be due to the invariance of the forces between colliding objects under this operation.
TL;DR: In this article, the application of finite-difference equations in the solution of repetitive multiloop resistive circuits in one-and two-dimensional configurations is discussed in both finite and infinite cases.
Abstract: The application of finite-difference equations in the solution of repetitive multiloop resistive circuits in one-and two-dimensional configurations is discussed in both finite and infinite cases. The technique of solution involves only ordinary algebra and trigonometry. Yet one can see the emergence of simple orthogonal functions and the finite-difference approximations of the Cauchy-Riemann equations and Laplace's equation. Boundary-value problems can be presented and understood at a simple level of physics and mathematics. Such repetitive structures can serve as discrete approximative models for various physical properties of continuous media. The implications for the teaching of boundary-value problems in electricity are brought out.